A layer of warm surface water of thickness 600m lies above colder deep water in the open ocean. In the surface layer the speed of sound is 1480ms−1, while in the deep layer it is 1520ms−1. A research vessel on the surface sends a brief ultrasonic pulse vertically downward and records the sea-bed echo after a total interval of 1.00s.
(i) Taking into account the two distinct sound speeds, set up expressions for the time taken by the pulse in each layer during the downward and upward journeys.
(ii) Hence calculate the total depth of the sea at that point.
(iii) If the ship’s equipment had incorrectly assumed a single uniform speed of 1500ms−1 for the whole path, by how many metres would the reported depth differ from the true depth found in part (ii)?